Abstract: Diaconescu, Moore and Witten have shown that the topological part of the M-theory partition function is an invariant of an E8 gauge bundle over the 11-dimensional bulk. Any construction of 11d SUGRA from gauge bundle data must satisfy a number of constraints in order to correctly reproduce the the known 10-dimensional physics on each boundary component. We analyse these constraints and in particular use them to attempt an approximate construction of the 11d gravitino as a condensate of the gauge theory fields.